# What conditions would allow planetary-sized objects to collide and remain intact?

I am modeling some off-the-wall scenarios to try out with a game engine.

One idea is trying to make a planet where some weird catastrophic incident has creates a funny shaped planet. I'm hoping to take advantage of differences in gravity, seasons, etc only I'm not sure this is physically possible in the first place.

For instance if two earth-sized planets collide being made purely of iron a star happens to forge in a crystalline structure favorable for impacts, what could be expected? Perhaps one of the objects could have been constructed by intelligent life and have a more specific structure if helpful.

What conditions could allow for a situation where two planetary objects have collided and maintain most of their individual shapes, at least temporarily?

If you have a planet of mass $M$, then its self-gravitational binding energy is roughly $-GM^2/2R$ give or take a small numerical factor. So, for the Earth, this would be $-2\times 10^{32}$ J.

Something colliding with the Earth, which has a similar mass and size, would do so at velocities of tens of km/s at least. I think the minimum closing velocity would be obtained by starting the two bodies at rest and allowing them to gravitationally accelerate each other. This would result in a kinetic energy of $\geq GM^2/2R$ (i.e. the planets start with zero gravitational potential energy at infinity, but would be separated by $2R$ as they collided). So it would seem that there is always enough kinetic energy available to unbind one and possibly both objects. It seems unlikely that such a collision could be anything but "catastrophic" for objects of similar mass.

Another way of thinking about this, is if I have an Earth-mass of pure iron, and each iron ion in a crystalline lattice has a heat capacity of $3k_{B}$, then the heat capacity of the planet would be $2.6 \times 10^{27}$ J/K. If I inject of order $10^{32}$ J into that system, and somehow keep it intact, it would be enough to raise its temperature by $10^{4}-10^{5}$ K, easily sufficient to melt iron.

• Unfortunately you paint a very solid picture, or perhaps I should say liquid. The difference in magnitudes is way way out of bounds for anything I can think of naturally or artificially correcting. – Garet Claborn Jul 16 '15 at 20:17
• @GaretClaborn Note that the energies depend on mass squared, whereas the heat capacity depends only on mass. – Rob Jeffries Jul 16 '15 at 20:26
• Ah ha. Is this the same as saying 'due to relativity between energy and mass, there would always be such a magnitude difference in the case of collisions?' – Garet Claborn Jul 17 '15 at 17:38
• @GaretClaborn No, it means smaller colliding objects might not get melted. – Rob Jeffries Jul 17 '15 at 22:36

Anything over 500 miles in diameter, give or take is almost always sphere-shaped, the primary variation being rotation speed, which can give a flatness to the object, for example, Jupiter is visibly flattened by it's high rotational speed.

The problem with building a strange shape by very large collision is that the heat generated in a collision of that size would almost certainly liquify the surface of the planet and anything liquid tends to be pretty smooth. For strange shapes, low gravity helps, and in the case of Mars with virtually no plate movement, volcanic eruptions can happen in the same location over a hot spot time and again for perhaps billions of years, which explains why Olympus Mons is 100 times larger than any similar formation on earth. It also doesn't hurt that there's a lack of erosion on mars due to no liquid/flowing water and very little atmosphere.

A high rotation speed and flattening of the sphere shape would also have the effect of short days and lower gravity around the equator than on the poles.